A study on maneuverability of a self-propelled crane barge at transit condition

Barge at Transit Condition

By:

Masayoshi Hirano*, Masahiro Fukushima*, Shuko Moriya* and Junshi Takashina'

This paper presents results of a study on the maneuverability of a self-propelled and large-sized crane barge at transit condition. The contents of the study consist of three major phases. In the first phase, the maneuverability of the subject shtp in calm water was investigated experimentally through extensive free running model tests and full scale trials. Then, in the second phase, an attempt was made to develop the prediction method of the maneuvering motion of ships such as the subject ship utilizing the digital computer simulation technique. The computed results were compared with the results of both the free running model tests and the full scale trials, mentioned above, and encouraging results were obtained for the validity of the prediction method developed in this study. In the last phase, wind effects on the maneuverability were investigated through simulation calculations in connection with the huge superstructure above water line and relatively low shzp speed at transit condition.

1. Introduction

The study on the maneuverability for marine structure is one of the important subjects to be investigated in the maneuverability field, as recommended by ITFC Maneuvering Committee1. The authors recently had a chance to investigate the maneuverability of a marine structure at transit condition. The marine structure, mentioned above, is a self-propelled and large-sized crane barge, built at Tamano Works of Mitsui Engineer-ing and ShipbuildEngineer-ing Co., Ltd. (MES). She consists of deck part, floater part of twin hulls, and columns which

connect the deck and the floater part, as shown in

Photo 1. Two kinds of large-sized cranes are mounted on the deck. She is a semi-submergible marine structure with draft deepened to the column position at operating condition. At transit condition she becomes a cata-maran, reducing draft to the floater position, which consists of twin floaters with propellers and nozzle rudders.

The study in this paper, on the maneuverability of the subject marine structure at transit condition, con-sists of three major phases. At first, the maneuverability in calm water was investigated experimentally through extensive free running model experiments and full scale trials. Next, the prediction method of the maneuvering motion of ships such as the subject ship was developed utilizing the digital computer simulation technique. Using scale models, the hydrodynamic and aerodynam-ic data required in the simulation were obtained by the rotating-arm tests and the low speed wind tunnel

* Marine Hydrodynamics Research Sect., Akishima Laboratory Technical Research & Development Hq.

-Photo i Full Scale Ship at Transit Condition

tests respectively. The computed results were com-pared with the results of both the free running model experiments and the full scale trials, performed in the first phase, and the validity of the prediction method was examined. In the last phase, wind effects on the maneuverability of the subject ship were examined through simulation studies based on the maneuvering motion prediction method developed in the second phase. Simulation calculations in wind for two typical maneuvering motions, namely turning motion and course keeping motion, were made, and the maneuver-ability under the wind condition was investigated in connection with the huge superstructure above water line at transit condition.

This paper describes the results obtained by these investigations, from both experimental and theoretical aspects, on the maneuverability of the subject marine structure at transit condition2>.

Hull L B (over all) B (demi-hull) d

J

AN A3 Propeller Pf a3

z

Full Scale Ship (m) 4.000 1.033 0.467 4 Model (a'=1.017) 2.200 1.603 0.485 0.186 0.345 0.075 0.800 0.700 4

Photo 2 Floater Part Model for Free Running Test

118.00 (m) 86.00 (m) 26.00 (m) 10.00 (KT) 54 600 (m2) 3 000 (m2) 4 575 tiOn zI Displacement of ship 8 Rudder angle ?fr Heading angle

Angle between wind direction and direc-tion of turning trajectory deviadirec-tion

lMAx Maximum angle of heading deviation in

course keeping motion Absolute wind direction P Density of water Pa Density of air 2. Experiments

2.1 Ship and Model Descriptions

The principal particulars of the subject marine struc-ture at transit condition, under which the full scale trials were carried out, are shown in Table i for floater part hull, propeller (impeller) and nozzle rudder. A 2.2 m long floater part model without superstructure above water line, shown in Photo 2, was made

cor-Table i Principal Particulars

NOTATION

AF Projected front area above water line

A_. Projected side area above water line a' Dimensionless space between demi-hulls

(=2B/L)

B Breadth of ship

BCTC Center to center distance between

demi-hulls

DL Lateral deviation in course keeping motion

DN Inner diameter of nozzle rudder Propeller diameter

d Draft of ship

I

Moment of inertia of ship with respect to

z-axis

Added moment of inertia of ship with respect to z-axis

J'

Dimensionless added moment of inertia of ship with respect to z-axis (=J/(I/2) pL4d)

K Ratio of absolute wind speed to ship ap-proach speed

L Length of ship

Chordwise length of nozzle rudder

m Mass of ship

m, m

Added mass in x and yaxes direction mr', m5' Dimensionless added mass in x and

y-axes direction (=m3, ni/(l/2)pL2d)

N Total yaw moment

n Number of propeller shaft revolution P Propeller pitch

QN Nozzle rudder torque

R Turning radius

r Yaw rate

r'

Dimensionless yaw rate (=_rL/V=L/R) SD Drifting distance

SA Apparent slip ratio

Thrust deduction coefficient U Absolute wind speed

u Ship speed in x-axis direction

u' Dimensionless ship speed in x-axis direc-tion (=u/V)

V Ship speed (=(u2±v2)"2) V Relative wind speed

Ship speed in y-axis direction

Dimensionless ship speed in y-axis direc-tion (==v/V)

w Wake fraction factor

X Total force in x-axis direction Nozzle rudder thrust

xn x-coordinate of point on which nozzle rudder force acts

Y Total force in y-axis direction

YN Nozzle rudder lateral force

YP y-coordinate of point on which propeller force acts

YR y-coordinate of point on which nozzle

rudder force acts Drift angle

fiR Geometrical inflow angle at rudder

posi-Nozzle Rudder

DN (m) 4.050 0.076

i-5

Fig. 1 Configuration of Afterbody (Body Plan)

( . -I

\J

'-p-- ui

___i, 5

of Afterbody (Profile)

responding to the full scale ship at transit condition. The space between demi-hulls of the model can be varied suôh as a' (=2BcTc/L)=0.800, 1.017 and 1.235 in order to examine the effects of a' on the maneuver-ability of this type of ships where the space of a = 1.017 corresponds to that of the full scale ship. Further-more an attempt was made to examine the effects of skeg which was supposed to be fitted at the stern end in the center piane of the floater, although this center skeg was not fitted on the full scale ship The principal particulars of hull propeller (impeller) and nozzle rudder of the model are also shown in Table 1. The hull configurations of the aft part of the left side floater are shown in Figs i and 2, where the skeg mentioned above is drawn by thick chain lines.

2.2 Free Ruhig Model Experiments

2 2 1 Contents of Model Experiments

The model experiments were carried out at the square basin of Ship Research Institute of Japan. The model ship was run with a radio control device. The ship motions (heading angle, yaw rate and drift angle) were measure

Wi, gyrosensers etc. and theasured data

were transmitted to the laboratory by telemeters equip-ped in the model. The trajectory of the maneuvering motion was obtained by the ship position detecting sys-tem with supersonic waves. The following tests were carried out fôr the three kinds of the space between demi-hülls, namely a'=0800, 1.017 and ì.23, where the skeg effects were investigated for a' = 1 017 case

only.

The model experiments were carried out with the ap-proach speed corresponding to approximate 5 knots of the full scale ship.

2.2.2 Results of Model Experiments (I) Turning motion

Some examples of the experimental results of the turning trajectories are shown with empty circles in

Figs 3-8, where each point of the empty circles denotes the: ship position (the center of gravity)

f

evei-y four seconds. Figs. 3, 4and 5 show that this type of ship is possessed of superior turning ability companng with that of the conventiönal type ship such as the oil tanker. Figs. 3, 4 and 5 also show that the effects of the space between demi-hulls on the turning ability are not con-spicuöus,

although the advance seems to become

somewhat larger as the space between demi-hulls be-comes wider. Comparing the turning trajectories shown in Figs. 4 and 7 with those shown in Figs 6 and 8, larger turning radius by fitting the skeg can be seen, especially remarkable difference can be seen between

the case of =l0° shown in Figs 7 and 8

This fact indicates skeg effects in increasing the turning

resist-ance.

Fig. 3 Turning Trajeotory (a'=0.800. 8=300)

Fig. 4 Turning Trajectory (a'=1.017, 8=30°)

\

A.E. A.E.&X 1 (1) (2) (3) turning tests :

zigzag maneuver tests: reversed spiral tests

=±3O°, +5°, ±20°,

l5°, ±1Ó° and 5°

1r=20°-20°,

Êig. 5 Turning Ïrajector' (ä'=1.235, 8=30°)

a'-j .017

Skeg Fitted

Fig. 6 Tûrning Tràjectory (à'=1.017, SKEG FITTED,

8=30°) a'=j.017 tl10' SIL - l'redjiction O Model Exp. Prediction O 'lodel Exp.

Fig. 7 ¶urnin9 Trajéctory (à'=i.017. 8=10°)

The experimental results of the time, histOries of heading angle, yaw rate, drift angle and ship speed from the time Of rudder execution in the turning motion are shown in Fig 9, as a typical example, for the case of a = 1 017 with =- 30° Larger yaw rate and drift angle than those of the conventional type ship, related to the above-mentiOned superìör turning ability, may be seen in this figure Some examples of the measúred results Of the forces and torque acting on the nozzle rudder (the port side hull) during turning motion are shown in

20 30

o

Fig. 8 Turning Trajectory (a'=1.017, SKEG FITTED, 8 =10°) °=L017. c=30 a==1.017 SIeg Fitted - Predict ott 6=10 Model Exp.

-Fig. 9 Time Histories of Heading Angle. Yaw Rate. Drift Angle and Ship Speed in Turning Motion (ä'=1.-017,6=30°) 0.2 a'=1.ÇJ17 . O ₆₀ t (s) 30 60 t(s) & 5 - 100 . - Prediction 10 -a. O AC Model Exp. o 30 60 - 90 t (s') 2.0 z 1.0 o o 0.4 500 0.2 - 400 300 Sc 10- 200 1.1) z - Prediction 2.0 -° Model Exp. 4.0- U.U5

î.

z - - 0.02

0í°--° ;

..

- 0

)JO

Fig. 10 Nozzle Rudder Forces and Torque in. Turning Motion (a'=1.017, 6=30°)

Figs. 10-13, where the definitions of the forces and torque should be referred. to the coordinate system shown in Fig. 31. Comparing the time histories of the nozzle rudder forces and torque shown in Fig. 10 with the corresponding time histories of the ship motioñ shown in Fig 9, it may be understood that nozzle rud-der forces and torque vary depending not only on the nozzle rudder angle itself but also on the ship motiOn.

o 0.1 be z X E

-2.0°°°

.?'-Fig. 11 Nozzle Rudder Forces and Torque in Turning Motion (a'=1.017, &=1O°)

0.2'-o

f-o.i

30 60 t(s) -. . . . -30 60 t(s) Prediction 2.0- ' Model Exp. il=1 .017 Skeg Fitted 60 t (s) -Prediction o Model Exp.

on,.

9 y --0.02 2.0 z 1.0 z X 30

''0' t(s)

- -6e.

t.s.

z -2.0 0.04 .02 oo 1(s)

Fig. 12, NozIe Rudder Forces and Torque in Turning Motioh (ä'-=L017, 'SKEG FITTED, 8=30°)

-2.0 - -- - - J-0.02

Fig. 13 Nozzle Rudder Forçe and Torque in Turning

-Motion (a'='1.017. SKEG FITTED7-8=--10°)

z

z

(2) Zigzag Maneuver Response

Some examples of the experimental results of the zigzag maneuver responses are shown with empty cir-cles in Figs 14-19. Very large overswing angle, com-paring with that of the. conventional type ship, can be seen in the heading angle responses for the -cases of the skeg not fitted as shown in Figs. 14, 16, 17 and 18, while the overswing -angle becomes moderate and the head ing angle response becomes quick by fitting the skeg as shown in Figs. 15 and 19. The measüred resUlts of

40

20

'-40

'-60

Fig. 14 20°--20° Zigzag Maneuver Response (a'=1.017)

40 20 be a'e=l .017 Skeg Fitted 20'-20Z Prediction o Model Exp. ollO 150 t(s') Prediction à Model Exp.

Fig. 5 20-20° Zigzag Maneuver Response (a'=1.017,

SKEG piTTED)

10- 1OZ

-60

Fig 16 10_10° Zigzag Maneuvér Response (a'=0.800) 5 30 60 - 90 t(s) o I--0.1 --1.0 -Prediction 2.0 Model Exp. 0.02 z9. E ox 30 6 g t('s) > 0.-b' 120 - 150 t(s) 0 -20 E z z -40 -60 0.2- a'1.017, 2.0 a'=l .017 0.2 Skeg Fitted 'f o.' >< z z 1.0 z z o 1.0 0.02 _E z O a"=1 .017 20-20Z. 60 0.1 be z 0 0.lt -0.2 4.0 E

the nozzle rudder forces and torque during the zigzag maíieiiver are shown in Figi.. 20 and 21, as typical examples, for the 10100 zigzag maneuver of both cases of the skeg not fitted and the skeg fitted.

('3) Steady Turning Performance

The experimental results of the steady turning per= formances obtained from both the turning tests and the reversed spiral tests are shown with empty circles

in Figs. 22-z-25. Small amount of unstable loop width can be seen for the cases of the skeg not fitted as shown

40

20

40 60

Fig. 17 10°-10° Zigzag Manuever Response (a'=1.017)

Fig. 18 100_100Zigzag Maneuver Response (a'=1.235) = 1. 017 10. 10Z a'=l. 017 'Skeg Fitted 10.-10.z Prediciiori o Model Exp. 151) (s) P red le ion o Model Exp. 60

Fig. 19 10°-10° Zigzag Maneuver Response (a'=1.017.

SKEG FITTED)

in FIgs. 22, 23 and 24, and the effects of the space be-tween demi-hulls on the unstable loop width may nOt be conspicuous. Together with the results for the turn-Ing motion shown in Figs 3, 4 and 5, and the results

so 1-0.1 0.1 0 0. L 2.0 2.0 2.0 30 60. 90 120 t(s)' 00 30

,60

a'=O. 800 30 20 1)) 120 I(s) - Predictithi o Model Exp. 90 o00 _120t(s) 1.0 o -1.0

Fig. 21 Nozzle Ruddér Forces' and Torque in Zigzag

Maneuver (a'=1.017. SKEG FITTED, 10°-10°Z)

Prediction Model Exp. z X z

z

z

1.5

Fig.' 22 steady Turning Performñce (ä'=0.800) Fig. 20 Nozzle Rudder Forces and Torque in Zigzag

Maneuver (a'=1.017, 10°-10°Z) 1. 017 0.2- Skeg Fitted j2.0 - - 10'-40Z I z i 0.F o _{'60 'gò 10 t(s)} O 0.2'- _{a"=1.017, 101OZ} 2.0 - Prediction o Model Exp. -2.0 0.02 E z 0.02

a=1. 017

30 20

10

Predict ion

1.0

O Model Exp..

Fig. 23 Steady Turning Performance (a'=1;017)

a'=l .235

1.5

- Prediction o Model Exp.

Fig. .24 Steady Turning Performance (a'=1.235)

a'=l .017

Sieg Fit tedi

30

20

10 1.0 0.5 0.5 Prediction 1.0 1.5 ii) 20 30 (deg) o Model Exp.

Fig. 25 Stead, Turning Ferforrnance (a'=1.Ó17, SKEG

FITTED)

for the zigzag maneuver response shown in Figs. 16 17 and 18, it may be mentioned from Figs 22, 23, and 24 that the effects of the space between demi-hulls on the maneuverability of this type of ship are not nOtice-able. On the other hand, comparing the steady turning performance shown in Fig. 23 with that. shown in Fig 25 remarkable improvement on the course keeping ability by fitting the skeg can be understood This fact may also be seen in the results of the zigzag ma neuver respOnses mentiOned before.

2.3 Full Scale Trials

The following tests were carried out in the full scale trials.

turning tests : 6= ±300 and ±20°

zigzag maneuver tests: 8fr= lO°l0

reversed spiral tests

The ship motions (heading angle, yaw rate and ship speed) were measured with gyrosensers prepared for this purpose. and with log equipped on the ship. Some typicâl examples of the full scale triál results are shown in Figs. 26--3O. The result of the turning trajeôtory for 8=30° is shown in Fig 26, where each point of the empty circles denotes the ship position of every twenty seconds. The time histories of heading angle, yaw rate and ship speed in the turning mòtioñ of 8=30° are

(5 500 2-400 o __.300 -a. 1.0- 200 -a. o -100 o 6=30 Prediction

0 Fall Scale Trial

Fig. 26. Turning Trajectory (Full Scale Ship, 8=300)

000

o o o o 00 o 0'

000000000

-Prediction

oo OFull Scale Trial

tnn)

Fig. 27 Time Histories 6f Heading Angle, Yaw Rate and Shr Speed in Turning Motion (Full Scale SlÍip, 8=30°)

io

shown in Fig. 27. The steady turning performance of the full scale ship obtained from the turning tests and the reversed spiral tests is shown in Fig. 28. In this figure no unstable loop width is found, while small amount of unstable loop width is seen in the model experimental results as shown in Fig. 23. Fig. 29 com-pares the steady turning performances of both the model ship (a'-=l.011) and the full scale ship. The results of the K- T analysis of the zigzag maneuver for both the model ship (a'= 1.017) and the full scale ship are shown

in Fig. 30 taking dimensionless mean yaw rate in

abscissa, where the results of the skeg-fitted model ship are also shown. Some amount of difference be-tween the results of the model experiments and those of the full scale trials may be seen in Figs. 29 and 30, and it may be mentioned that the performance of the full scale ship is between those of the modèl ships with the skeg fitted añd the skeg not fitted. Generally the scale effect due to the propeller load differençe could cause the discrepancy between the full scale trials and

1.5 1.0 0.5 1.5 1.0 0.5 -1.0 Prediction

o Ful! Scale Trial

-1.5

Fig. 28 Steady Turning Performance (Full Scale Ship)

-30 -20 -10 1 io 20 - 30 8 (dog)

-0:5

0-Model Exp. (a'=i.017)

Full Scale Trial

-1.5

Fig. 29 Comparison of Stèady Tùthing Perfórmahce between Model and Full Scale Ship

0.8

0.6

0.4

11.2

1/K'

Full Scale Trial

/A

A

7

-.ó-- Model Exp. (a'1.017)

-«o--Do. (a'i-.017, Sieg Fitted)

o

0.1 02 0.3 0.4 .0.5

Fig. 30 Comparison of 1/K', lIT' between Model and Full Scale Ship

the model experiments, but this can not explain the discrepancy mentioned above

The reason for this

discrepancy is not clear at the present stage. As one of possible explánations, it may be able to point out the possibility that the hydrodynathic forces df the full scale ship differ from thOse of the model ship due to lacking of the miscellaneous appendages such as anchors etc. at bow and stern on the hull of the full scale ship.

3. Maneuvering Motion Predictiou 3.1 Mathematical Modél

3.1.1 Equations of MOtion

A set of coordinate axes with origin fixed at the

center of gravity of the ship, as shown in Fig 31 is

used to describe the ship maneuvering motion. Longi-tudinal and transverse, horizontal axes are represented by the x and y-axes. By refçrençe to this çoordinate system, the equations of motiôn can be written in the following form.

Surge:

m(ii-vr)=X

Sway: m(i,+ur)= Y

(1).

YaW

Ír

=N

where X, Y and N denote total hydrodynamlc forces generated by ship motions, propellers (impellers) and nozzle rudders. The hydrodynamic and aerodynamic terms can be expressed in the form

X=XH+Xp±XR±XW Y=YH-f-Yp+YR±Yw

(2)

N = NH+Np ± NR ±.N 10 20 30 5(dcg) -30 -20 -10 lIT'

₇

.7

11.2 0.3 0..l 0.5

Fig. 31 Coordinate System

where the terms with subscript H, P, R and W represent hydrodynamic forces produced by ship motions and

acting on ship hull (hull

forces), propeller forces, nozzle rudder forces, and wind forces respectively. 3.1.2 Full Forces

The hull forces are expressed in terms of dimension-less quantitics such as

N'-

NH

"

pLdV

(3)

The longitudinal force XH' can be written in the form3

Xff'= -mz'ü'+(my'+Xvr')v'r'+X'(u')

+Xvo'V'2±1rr''2

(4)

The lateral force H' and the yaw moment NH' can be written ¿n the following form employing the third power polynomiäh Of the hydrödynamic fôrce deriva-tives.

m- m,'i,' - ,n'u'r / + Y'v' + Y,'r'

+

Yvvo'V'8 ± Yvvr'V'2r'

-4- Y'v'r'2-f- Y,.rr'r'3 NH' = m.Tzz't' + N'v' + Nr'r'

+ tT'v'3 + ITvvr'V'2 r' -j- !sTvrr'v'r'2 +1Trrr''8

The added inertia terms in equations (4) and (5), namely mi', m' and were determined by making use of the estiiflate charts given by Prof. S. Motora4, and the estimated results are shown in Table 2 The hydrodynamjc force derivatives with rçspect to y' and r' in equations (4) ánd Were obtained based on the results of the hydrodynamic force measurement tests by the rotating-arm test device at Kyushu University of Japan, which were carried out ùsing the same model ship as that described in 2.1 for four cases of conditions,

X'

E,

yXHYir

Table 2 Hydrodynamic Force Derivatives

namely three cases of the space between demi-hulls (a'= 0.800, 1.017 and 1.235) and the case of the skeg fitted (a'=l.017). The derivatives determined from the hy-drodynamic force measurement test results with the least-square fitting technique are summarized in Table 2. The ship resistance coefficients X'(u') were estimated using the resistance test results carried out at Akishima Laboratory of MES.

3.1.3 Propeller Forces

The propeller effective thrust, the lateral force and the yaw moment due to propellers can be written

=

=

(1 - tpj)pnJ2DP4KT(.Jpj)

YE = O

N=- XPJYPI

= -

1çl -tPf)pnf2DP4KT(JP) y?1

where j =1 and 2 represent the propellers of the port and the starboard side hull respectively.

Referring to the nozzle propeller test results at NSMB5, the thrust coefficient K(J1) in equation (6) can be estimated by

KT(Jp .1) =

(7)

where the advance coefficient J is expressed

Jp1u(lwp1)/nDp

(8)

A. in equation (7) is a constant determined by the

prinòipal particulars of propeller.

9

a'=O.800 a'=1.017 a'=1.235 -SKEG FITIED (a'=l.Olj) m/m 0.120 0.120 0.120 0.120 mr/rn 0.820 0.820 0.820 0.820 J,,/mL2 0.027 0.030 0.034 0.030 I,,/mL2 _{0.109 0.127 0A47 0.127} (m+X,,,)/m, 0.160 0.194 0.229 0.359 X,,,,' 0.0 0.0 0.0 0.0 X,,' -0.063 -0.070 -0.077 -0.079 Y,,' -0.727 -0.739

-0.72

-1.029 Y,' 0.362. 0.366 0.370 0.468 Y,,,,,' -4.860 -4.940 -5.018 -1.766 Y,,,' -0.017 -0.013 -0.009 -0.083 Y,,,,' -1.360 -1.408 -1.453 -0.819 Y,,,,' -0.237 -0.318 -0.400 -Ò.153 N,,' -0.235 -0.254 -0.272 -0.Ï93 N,' -0.074 -0.086 -0.098 -0.114 N,,,,,' 0.464 0.487 0.501 0.096 -0.008 -0.010 -0.009 -0.001 N,,,,,' -0.181 -0.184 -0.188 -0.428 N,,,' 0.048 0.056 0.043 -0.016

3.1.4 NOzzle Rudder Forces

Referring to Fig. 31 the longitudinal force, the lateral -force and the yaw moment generated by the nozzlè rudders can be written in the form

XR=±XNjcOSô+Y.fsifl8

2 2

YR= XNJSifl8± YNJcos8

J1

j=i

NR= YRxR (XNjcos8 + YNI sin 8)YRJ

where 1NJ and YNJ represent the thrust and the normal force acting on the nozzle rudder itself respectively. Subscripts j= I and 2 répresent the port nozzle rudder and the starboard nozzle rudder respectively.

Let us introduce dimensionless forms such as

X, Yi

+ (O.77Tn1D)2} D 'N (lo)

-

QNJ XNJ', YNI'-!NJ p{u2±(O.7lrnJDp)2}Dp!N2 J

where the nozzle rudder torque Q/ is added.

Based on the results of the nozzle rudder force

measurement tests in the behind hull condition by the rotating-arm test device at Kyushu University, X', Y' etc. were estimated. Figs. 32 and 33 show experi-mental data of. YN1' and QN1' at the propeller working point of S4=O.628 (in term of the apparent slip ratio) for the various combinations of the geometrical infloW angle at the rudder position fiR and the rudder angle

8. Sithilar results to those shown in Figs. 32 and 33

were obtained for different points of 5A These facts may suggest that the nozzle rudder forces could be considered as functions of 54, fiR and ,that is

XNJ'=XN/(sAj, fl, 8)

V '_V '1

¡2

NJ - NJ

Aj' PR» QN/=QNJ'(sAj, fl, 8) where

sA=l.

u XRr (12) fl.P L

The curves such as those drawn in Figs. 32 and 33 were used m the nozzle rudder force calculation. 3.1.5 Wind Forces

Let us introduce dimensionless forms such as

X'

W N L V,2 - 30 .11 n? 50 °-20 Jj Fig. 32 r fr I -° 10 20 30 4 SAO. 628. 0 a'l .017 s =0 628 o

50 40 30 20 10

a--50 40

0 -

-:o

000

I I t J.

50 40 30 ..0

O 40 I 0.8

00

o

Normal Force Coefficient (s= 0. 62 8) .6 0.8--1.0 -5=30. fi, (dog) 40 50 - Iò=10. o O

Fig. 33 Torque Coefficient of Port Nozzle Ruddär (SA= 0.628)

of Port Nozzle Rudder

0-0 /3 50

30 40/350

6=-10

6=-3o

Photo 3 - Superstructure Modél for Wind Tunnel Test

1.0 a'1.017

Fig. 34 Wind Förce Coefficient (in x-direction)

Fig. 35 Wind Force Coefficient (in ydirection)

180

Fig. 36 Wind Moment Coéfficient (about z-axis)

The wind force coefficients X' etc. in equation (13) were obtained based on the results of the wind fOrce measurement tests, which were carried out using a model of superstruòture above water line of 1/250 scale, shown in Photo 3, at the low speed wind tunnel of Akishima Laboratory of MES. The measured results used in the wind force calculation arc shown in Figs. 34-36 taking the wind direction in abscissa. 3.2 Numerical Results and Discussibns

A series of computations corresponding to the es1ts of the model experiments and the full scale triâls shown

in Figs. 3-28 were carried out using the mathematical model combined with the hydrodynamic data described in 3.1. The computed results are shown with solid lines in these figures.

At first, comparisons with the model experimental results are made. It may be seeñ from Figs. 3S that the computed results of the turning trajectories general-ly show good agreement with the experimental ones. GoOd agreement may also be seen for the time histories in the tûrning motion as shown in Fig. 9. The computed results of the zigzag maneuver responses agree well with the experimental ones as shown in Figs. 14-19, especially fairly good agreement can be seen in the cases f the skeg fitted. As for the steady turning perform-ances, the computed and the experimental results are also in a good agreement. The remarkable improve-ment on the course keeping ability by fitting the skeg is explained satisfâctorily by the calculation as can be seen inFigs. 23 and 25. The computed results of the nozzle rudder forces and torque agree comparably well with the experimental results as shown in Figs. 10-r-13, 20 and 21, although some amount of discrepancy may be seen in the torque variation.

Next, let us make comparisons of the computed re-sults with the full scale trial rere-sults,. The same. hy-drodynamic force derivatives as those of the model ship of a' = 1.017 were used in the computation of the full scale maneuvering motions. It may be considered that the computed and the full scale trial results general-ly show encouraging correlations as seen in Figs. 26-28, although some amount of discrepancy may be seen in these figures. Regarding this discrepancy the same kind of discussion as that for the difference between the results of the full scale trials and the model ex-periments, mentioned in 2.3, may be made.

It may be concluded from the facts, mentioned here, that the prediction method of the maneuvering motion developed in this study would be useful for the analysis of the' maneuverability of ships such as the subject marine structure at transit condition

4. Wind Effects on Maneuverability

Based on the mathematical model combined with the hydrodynamiô and aerodynamic data, described in 3.1, the wind effects on the maneuverability of the sub-ject marine structure at transit condition were examined through simulation calculations in connection with the huge superstructure above water line. The projected front and side areas above water line, AF and A, used in the simulation are:.shown in Table 1. Since the effects of the space between demi hulls on the maneuverabihty were not conspicuous as mentioned in 2.2, simulations here were made only for the case of a'= 1.017.

4.1 Turniñg Motion ¡n Wind

The turning motions in wind were computed for the following combinations of ship and wind conditions.

(1) ship approach speed: V=5.0 knots

(2). rudder angle

8=-30°, 20g and 10°

(port turning only)

wind speed U lO,

20, 30 and 40

knots, namely K (.=U/V0)=2, 4, 6 and 8 wind direction =45° 900 and 1350

.skeg : not fitted

The computed results of the turning trajectories in wind of.the wind speed of K2, 4 and 6 with the Wind direction of !kw=90° are shown in Figs 37, 38 and 39

respectively for the rudder angle of ¿'= 30°, as typical examples. The simulation results, show that the ship can not turn in the case of the wind speed of K=8. The deviation pattern of the turning trajectories in Wind can be understood from these figures, and it may be seen that the ship would meet considerable difficulty in the turgig motion under the wind condition of the wind speed of K=6. The computed results are sum-marized in Fig. 40 in the form of the drifting distance

5D which is defined as the quantity of the deviation of

the turning trajectory during one round (360°) turning, and in Fig. 41, in the form of the angle between the

x/L

Fig. 37 Turning Trajectory in Wind (fr=900. K=2 8=-30°)

Fig. -38 Turning Trajectòry 1h Wind (rw90°. K4, 8=_300)

Fig. 39 Turning'Trajectòry in Wind (yw=9O°. K6, 8=_300) 10.0 5.0 1.0 0.5 0.1 210 Ï80 150 SD/L Wind SD 5= - 30 -

----i

-- - _K 2 4 6 8

Fig. 40 brifting Distance in Wind

çbD (deg) 240-Wind 5=- 1o = -?0 - 30 - 120. T-

---

_K o 2 - 4

Fig 41-D'eion of D'evation of Turning Trajectory

wind direction and the direction of the deviation D The drifting distance only for the case of _3Øo

is shown in Fig. 40 because almost similar results

are obtained for the other cases of the rudder angle. As easily can be understood from the definition, 5D

and in Figs 40 and 41 do not depend on the original wind direction The computed turning trajectories in wind for the case of the skeg fitted, not shown here, have similär tendency to those for the case of the skeg

not fitted, mentioned above.

4.2 Course Keeping Motion in Wind

Simulation runs for the course keeping mOtion in wind were made for the following combinations of ship and wind condition.

ship approach speed V=5.O knots wind speed K=2, 4, 6 and 8 wnd direction

k=45°,

9Ø0

and 135° skeg both cases of not fitted and

fitted

. Supposñg that the wind force would start acting on

the ship at the time of t==O as a step function (steady wind), the course keeping motion with automatic rud-der control were computed. The following PIDlaw of the rudder control was employed in the simulation.

TI o

(l4) where the desired heading angle was supposed as O, and the rudder angle controlled by equation (14) was lithited ñot to exceed 181=15°.

Some examples of the computed results for time histories of heading angle, rudder angle, lateral devia-tion and ship speed from the time of t=O to the time when the ship enters into the steady state condition, are shown in Figs 42-48 The control gains used in these

computations are such as K=l.0, T=60.0 and T1=

100.0. The change in the ship response patterns when the wind speed increases may be understood from Figs. 42, 43 and 44. The coutse keeping operation cannOt

be realized in the case of the wind speed of K=8

namely some amount of deviation of the heading angle remains at the steady state condition as can be seen in Fig. 44: Comparing the results shown in Figs. 45 and 46 with the result in Fig. 43, the change in the ship response patterns When the wind direction varies may be understood. Large amount of the lateral deviatiOn can be seen in the case of the bow wind of fr,=45° comparing with that in the case of the beam wind of fr=9O°. The course keeping operation becomes diffi

cult greatly in the quartering wind of k=l35° as

shown in Fig. 46 where large heading angle response at the steädy state condition may be seen. The skeg effects in the course keeping motion under the wind condition can be understood from Figs. 43, 44, 41 and 48, where less heading and rudder angle responses can be seen iñ the case of the skeg fitted. The improvement of the course keeping ability by fitting the skeg was confirmed not only iñ the form of the steady turning performances in calm water but also in the simulations

c"w=9O K=8

IJL/L V

(ko t)

IO

4 2

Fig. 42 Time Histories of Course Keeping Motion ¡n

Wind (fr,=9O°. K=4)

Fig. 43 Time Histories of Course Keeping Motion in

Wind (ifrw=90°. K6) DL/L V (knot) 4 - t 2-5 iS 20 I. 4 t (mio)

2-3

Fig. 44 Time Histories of Course Keeping MotiOn in

Wind (kwr9O°, K8)

LiL/L V

(deg) (knot)

40 cÍ'tv45 K=6 - 4 6

40

4 2

40

4 5

Fig. 45 Time Histories of Course Keeping Motion iñ

Wind (fr=45°. K6) (deg) çOw=13F K=6 20

20

4ò

(deg) 40

20

ÇiO K=6 SKIC FITTED lo lo DL!!. \' (knot) 4-6

2-3

4---2

Fig. 46 -Time Histories of Course Keeping Mótion 1h

Wind (fr=135°, K=6) 20 2, 5 Dt/L V (knot) 4ml

40

4 2

Fig. 41 Time Histories of Course Keeping Motion in Wind (fr=90°, K=6. SKEG FITTED)

(dog)

=90 K=8

SKEG FITTED

-20

20

Fig. 48 Time Histories of Course Keeping Moton ih

Wind fr=90°. K=8, SKEG FITTED)

of the course keeping motion with automatic rudder control in wind.

The resi.ilts of the simulation runs are summarized in Figs. 49-52. Fig. 49 shoWs the maximum heading angle which is the first peak in the time history of /r

The rudder angle and the ship speed change at the steady state condition are shown in Figs. 50 and 51

respectively. Fig. 52 shows the lateral deviation when the ship sails one mile. In these figures the solid marks mean that the cOurse keeping operation can not be realized, and this fact may be noticed in Fig 50 where the rudder angles at the steady state cor dition with solid mark are saturated to 15°. The effects of the wind speed and the wind diréction on the coúrse keeping mo-tion including the skeg effects can be clearly under-stood from these figures.

The results obtained from simulation runs with one typical combination of the control gains of automatic rudder control are shown and discussed above. Similar

1w= 45O bwr 90O w 135 6 L ÇbMAX(deg) 12 SKEG FITTED 10 çbw=

45ø-w= 90O-= çbw = 135 .-. DL/L V (knot)

46

2. 5 20 4 (mm)

Fig. 49 Maximum Angle of HeadFng Deviation ih

Course Keeping Motion

-2-5

15 20

1.0 -. 1.0 çtw= 45-O tw= go-ô-'w= 135-.8-. Vs/Vo SKEG FITTED t_t t ç"w= 450-V'w 9O 0.0

2468

K 0.0

2468

Fig. 51 Ship Speed Çhange at Steady State Condition in Course KeepingMótiòn

results were obtained qualitatively for other com-binations of the control gains It may be considered from these sirnulatioñ results that the maneuverability of the subject ship could be influenced remarkably by wind in connection with the huge superstructure above water line and relatively low ship speed at transit con-dition.

5. Concluding Remarks

The maneuverability of a self-propelled and large-sized crane barge at transit condition were studied in

this paper from both experimental and theoretical

aspects. The major conclusións obtained in this study are summarized as follows.

DL/L

10

10

(I) The subject ship is possessed of superior turning ability comparing with that of the conventional type ship. As for the course keeping ability, small amount of unstable loop width may appear in the steady turn-ing performances.

The prediction method of the maneuvering mo tion developed in this study would be useful for the analysis of the maneuverability of ships such as the subject ship.

The results of the simulation runs for the maneu-vering motion in wind show that the maneuverabihty of the subject ship could be inflUenced remarkably by wind in connection with the huge superstructure above water line and relatively 1w ship speed at transit con-dition.

The effects Of the skeg, fitted at the stern end in the center plane of the floater, on the course keeping ability are remarkable, as confirmed not only in the form of the steady turning performances in calm water but also in the simulations of the course keeping motion in wind.

References

The 15th ITTC Maneuvering Committee Report, (1978) M Hirano Y Yanianouchi M Fukushima S Moriya A Study on Maneuverability Of a Self-Propelled Marine

Structure at Transit Condition, Proceedings of International Symposium on Ocean EngineeringShip Handling, SSPA,

(1980), p.10:1

A. Ogawa and R Kasai: On the Mathematical Model of Maneuvering MOtion of Ships. ¡SP, 25, 292 (1978) p. 306

S. Motora: On the Measurement of Add&1 Mass an

Added Moment of Inertia for Ship MOtiOns (Part 1, 2 añd

3). Journal Of Society of Naval Architects of Japan, Vol.

105 106, (1959 1960) (in Japanese)

M. W. C. Oosterveld: Investigations on Different Pro. peller Types. ISP, 18, 198 (1971), p. 32

DL/L Skeg Fitted frw=45 Ø sw=9O -o-=

l35-ô--t

2 4 6/8 K 15

Fig; 50 Rudder Angle at Steady State Condition in Fig. 52 Lateral Deviation at One Mile Sailing in

Course Keeping MotiOn Course Keeping MotiOn